Lambert's W, infinite divisibility and Poisson mixtures |
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Authors: | Anthony G Pakes |
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Institution: | School of Mathematics & Statistics, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia |
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Abstract: | The Lambert W function is shown to be the Laplace exponent of a positive infinitely divisible law (i.e. W is a Bernstein function) called the standard Lambert law. This law is a generalized gamma convolution. At least three Poisson mixture families are defined in terms of W. One of these is the generalized Poisson laws which are shown to be generalized negative-binomial convolutions. Mixing with positive stable laws yields further generalizations. |
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Keywords: | Lambert W function Infinite divisibility Poisson mixtures Generalized convolutions Stable laws |
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